Preheat oven to 425 degrees F.
In a large mixing bowl, beat together the butter, applesauce, and sugars until creamy.
Add eggs and beat well to incorporate.
Mix in the baking powder, baking soda, cinnamon, nutmeg, cloves, and salt.
Alternate adding the flour and the cider, mixing well after each addition. Start and end with the flour, scraping the sides of the bowl before the final mix. The batter will be quite thick!
Pipe the batter into lightly greased doughnut pans. Fill the wells almost all the way to the top, but not quite. You want a bit of room for the doughnuts to rise!
Bake for 9 minutes, then turn out of pan immediately. Dip the doughnuts into melted butter, then toss in cinnamon sugar mixture. Enjoy!
